The Divide-and-Conquer Manifesto

Existing machine learning theory and algorithms have focused on learning an unknown function from training examples, where the unknown function maps from a feature vector to one of a small number of classes. Emerging applications in science and industry require learning much more complex functions that map from complex input spaces (e.g., 2-dimensional maps, time series, and strings) to complex output spaces (e.g., other 2-dimensional maps, time series, and strings). Despite the lack of theory covering such cases, many practical systems have been built that work well in particular applications. These systems all employ some form of divide-and-conquer, where the inputs and outputs are divided into smaller pieces (e.g., "windows"), classified, and then the results are merged to produce an overall solution. This paper defines the problem of divide-and-conquer learning and identifies the key research questions that need to be studied in order to develop practical, general-purpose learning algorithms for divide-and-conquer problems and an associated theory.